Changeset fac3ec in git

Timestamp:

Jun 3, 2020, 4:05:24 PM (3 years ago)

Author:

Hans Schoenemann <hannes@…>

Branches:

(u'spielwiese', '91e5db82acc17434e4062bcfa44e6efa7d41fd30')

Children:

c2b991812d200ff53e5b84053d8ed56c0e2c51a0

Parents:

6f25ae1c3ecfd4dbc7f6815716b2cb7ab4644d9d

Message:

new grobcov.lib

File:

• Singular/LIB/grobcov.lib (modified) (87 diffs)

Singular/LIB/grobcov.lib

@@ -1 +1 @@
 //////////////////////////////////////////////////////////////////////////////
-version="version grobcov.lib 4.1.2.  January_2020 "; // $Id$;
-           // version N9;  January 2020;
+version="version grobcov.lib 4.1.3  January_2020 "; // $Id$
+           // version N10;  June 2020;
 info="
 LIBRARY:  grobcov.lib
@@ -120 +120 @@
           hypothesis and thesis in ADGT.
 
-          This version was finished on 1/2/2020,
+          This version was finished on 26/5/2020,
 
 
@@ -247 +247 @@
           determines a CGS in full-representation using WLemma
 
-intersectpar(L); Auxiliary routine. Given a list of ideals defined on K[a][x]
+intersectpar(L); Auxiliary routine. Given a list of ideals definend on K[a][x]
          it determines the intersection of all of them in K[x,a]
 
@@ -321 +321 @@
 // Release N9: December 2019. New routine DifConsLCSets,
 // Updated also ADGT to use as option DifConsLCSets
+// Release N10: May 2020.
+// Updated locus. New determination of the taxonomies
 
 //*************Auxiliary routines**************
@@ -964 +966 @@
         mu=mu*nu;
         rho=qlc[1]*qlm;
-        //"T_nu="; nu; "mu="; mu; "rho="; rho;
         p=nu*p-rho*F[i];
         r=nu*r;
         for (j=1;j<=size(F);j++){q[j]=nu*q[j];}
         q[i]=q[i]+rho;
-        //"T_q[i]="; q[i];
         divoc=1;
       }
@@ -979 +979 @@
       p=p-lcp*lpp;
     }
-    //"T_r="; r; "p="; p;
   }
   list res=r,q,mu;
@@ -1657 +1656 @@
     }
   }
-  //"T_before="; prep;
   if (size(prep)==0){prep=list(list(ideal(1),list(ideal(1))));}
-  //"T_Prep="; prep;
-  //def Lout=CompleteA(prep,prep);
-  //"T_Lout="; Lout;
   return(prep);
 }
@@ -1739 +1734 @@
   {
     option(returnSB);
-    //"T_Lp[i]="; Lp[i];
     N=Lp[i][1];
     Lb=Lp[i][2];
-    //"T_Lb="; Lb;
     ida=intersect(ida,N);
     for(j=1;j<=size(Lb);j++)
@@ -1954 +1947 @@
     def BH=imap(RR,B2);
     def LH=imap(RR,LL);
-    //"T_BH="; BH;
-    //"T_LH="; LH;
     for (i=1;i<=size(BH);i++)
     {
@@ -1967 +1958 @@
     def RPH=DH+PH;
     def GSH=KSW(BH,LH);
-    //"T_GSH="; GSH;
     //setglobalrings();
     // DEHOMOGENIZING THE RESULT
@@ -2101 +2091 @@
     P[i]=L[Q[i][1]][Q[i][2]];
   }
-  //"T_P="; P;
   // P is the list of the maximal components of the union
   //   with the corresponding initial holes.
@@ -2139 +2128 @@
   int i; int j; int k; list H; list C; list T;
   list L0; list P0; list P; list Q0; list Q;
-  //"T_L="; L;
   for (i=1;i<=size(L);i++)
   {
@@ -2148 +2136 @@
     }
   }
-  //"T_P0="; P0;
   Q0=selectminideals(P0);
-  //"T_Q0="; Q0;
   for (i=1;i<=size(Q0);i++)
   {
@@ -2156 +2142 @@
     P[i]=L[Q0[i][1]];// [Q[i][2]];
   }
-  //"T_P="; P;
   // P is the list of the maximal components of the union
   //   with the corresponding initial holes.
@@ -2264 +2249 @@
 static proc addpartfine(list H, list C0)
 {
-  //"T_H="; H;
   int i; int j; int k; int te; intvec notQ; int l; list sel;
   intvec jtesC;
@@ -2351 +2335 @@
 static proc needcombine(list LCU,ideal N)
 {
-  //"Deciding if combine is needed";;
   ideal BB;
   int tes=0; int m=1; int j; int k; poly sp;
@@ -2526 +2509 @@
       LCU[k][1]=B;
     }
-    //"Deciding if combine is needed";
     crep=PtoCrep(prep);
     if(size(LCU)>1){tes=1;}
@@ -3261 +3243 @@
   }
   combpolys=reform(combpolys,numdens);
-  //"T_combpolys="; combpolys;
   //setring(RR);
   //def combpolysT=imap(P,combpolys);
@@ -3975 +3956 @@
   {
     CG=KSWtocgsdr(CG);
-    //"T_CG="; CG;
     if( size(CG)>0)
     {
@@ -4369 +4349 @@
   {
     t=T[i];
-    //"T_t"; t;
     P=0; Q=1;
     for(j=1;j<=n;j++)
@@ -4383 +4362 @@
     }
     Cb=Crep0(P,Q);
-    //"T_Cb="; Cb;
     if(size(Cb)!=0)
     {
@@ -4472 +4450 @@
   {
     K=FirstLevel(B);
-    //"T_K="; K;
     L[size(L)+1]=K[1];
     B=K[2];
@@ -4593 +4570 @@
   if (size(B) mod 2==1){B[size(B)+1]=ideal(1);}
   if (size(A) mod 2==1){A[size(A)+1]=ideal(1);}
-  //"T_A=";A;
- // "T_B="; B;
   n=size(A) div 2;
   m=(size(B) div 2)-1;
@@ -4613 +4588 @@
       //string("T_j=",j);
       ABdw=intersectpar(list(A[2*i],B[2*j+1]));
-      //"T_ABdw="; ABdw;
       ABup=A[2*i-1];
-      //"T_ABup1="; ABup;
       if(j>0)
       {
@@ -4623 +4596 @@
         }
       }
-      //"T_ABup2="; ABup;
       ABupC=Crep(ABup,ideal(1));
-      //"T_ABupC="; ABupC;
       ABup=ABupC[1];
-       //"T_ABup="; ABup;
       if(ABup==1){t=0;}
      //if(equalideals(ABup,ideal(1))){t=0;}
@@ -4633 +4603 @@
       {
         M=Crep(ABup,ABdw);
-        //"T_M="; M;
         //if(not(equalideals(M[1],ideal(1)))) {L[size(L)+1]=M;}
         if(not(size(M)==0)) {L[size(L)+1]=M;}
       }
-      //"L="; L;
       j++;
     }
@@ -4751 +4719 @@
   attrib(NP,"IsSB",1);
   int d=dim(std(NP));
-  //"T_d="; d;
   if(d==0){te=0;}
   setring(RR);
@@ -4774 +4741 @@
  }
 
-//  DimPar
+//  DimComp
 //  Auxiliary routine to locus2 determining the dimension of a parametric ideal
 //  it is identical to DimPar but adds information about the character of the component
@@ -4855 +4822 @@
           // independent of parameters giving the variables with dimension 0
        dd=indepparameters(B);
-       //"T_dd="; dd;
         if (dd==1){d=0; L0=d,string(B);}  // ,determineF(B,F,E)
         else{d=1; L0=2,"Normal";}
@@ -4862 +4828 @@
       {
         def RH=ringlist(RR);
-         //"T_RH="; RH;
         def H=RH;
         H[1]=0;
@@ -4925 +4890 @@
       }
     }
-     //"T_L0="; L0;
     return(L0);
   }
@@ -4947 +4911 @@
   def RRH=ring(H);
 
-        //" ";string("Anti-image of Special component = ", GGG);
 
    setring(RRH);
@@ -4956 +4919 @@
    ideal M=std(AA+FH);
    def rh=reduce(EH,M,5);
-   //"T_AA="; AA; "T_FH="; FH; "T_EH="; EH; "T_rh="; rh;
    if(rh==0){env=1;} else{env=0;}
    setring RR;
           //L0[3]=env;
-    //"T_env="; env;
     return(env);
 }
@@ -5005 +4966 @@
   def D=ring(RX);
   def RP=D+P;
-  //"T_locus0 ha estat cridat";
   // if(defined(@P)==1){te=1; kill @P; kill @R; kill @RP; }
   // setglobalrings();
@@ -5099 +5059 @@
   } //In P1 factors in the basis independent of the parameters have been obtained
   ideal BB; int dd; list NS;
+  // "T_AQUI_3";
   for(i=1;i<=size(P1);i++)
   {
-     //"T_P1="; P1;
      NS=NorSing(P1[i][3],P1[i][1],P1[i][2][1],DD);
-     //"T_NS="; NS;
      dd=NS[1];
      if(dd==0){P1[i][3]=NS;}  //"Special"; //dd==0
@@ -5212 +5171 @@
 //              If all levels of a class of locus are 1, then the set is locally closed. Otherwise the level
 //              gives the depth of the component.
+// static proc locus2(list G, ideal F, list #)
 static proc locus2(list G, ideal F, list #)
 {
  int st=timer;
  list Snor; list Snonor;
- int d; int i; int j;
+ int d; int i; int j; int mt=0;
  def RR=basering;
  def Rx=ringlist(RR);
@@ -5224 +5184 @@
  list GG=G;
  int n=size(Rx[1][2]);
- int moverdim;
+ int moverdim=n;
  for(i=1;i<=(size(DD) div 2);i++)
   {
-     if(DD[2*i-1]=="moverdim"){moverdim=DD[2*i];}
+     if(DD[2*i-1]=="moverdim"){moverdim=DD[2*i]; mt=1; }
      if(DD[2*i-1]=="vmov"){vmov=DD[2*i];}
 //    if(DD[2*i-1]=="vmov"){vmov=DD[2*i];}
@@ -5233 +5193 @@
 //    if(DD[2*i-1]=="comment"){comment=DD[2*i];}
 //    if(DD[2*i-1]=="grobcov"){GG=DD[2*i];}
-    if(DD[2*i-1]=="anti-image"){tax=DD[2*i];}
-  }
+//    if(DD[2*i-1]=="anti-image"){tax=DD[2*i];}
+  }
+  if(mt==0){DD[size(DD)+1]="moverdim"; DD[size(DD)+1]=moverdim;}
  for(i=1;i<=size(GG);i++)
  {
@@ -5258 +5219 @@
    }
  }
- //"T_Snor="; Snor;
- //"T_Snonor="; Snonor;
  int tnor=size(Snor); int tnonor=size(Snonor);
  setring RP;
@@ -5275 +5234 @@
    SnonorP=LCUnionN(SnonorP);
  }
- //"T_SnorP after LCUnion="; SnorP;
-// "T_SnonorP  after LCUnion="; SnonorP;
  setring RR;
  ideal C;  list N;  list BAC; list AI;
@@ -5296 +5253 @@
      N=Snor[i][2];
      dimP=DimPar(C);
-      //"T_G="; G;
      AI=NS(F,G,C,N,DD);
-     //"T_AI="; AI;
      AI0=AI[2];
      if(size(AI)==3){AI[2]="normal"; AI[3]=ideal(0);}
      else
      {
-     if(AI[1]>=dimP)
-     {
-       AI[2]="Normal";
-       if(tax>0){AI[3]=AI0;}
-     }
-     else
-        {
-           //"T_Al=";
+       if(AI[1]>=dimP)
+       {
+         AI[2]="Normal";
+         if(tax>0){AI[3]=AI0;}
+       }
+       else
+       {
            if(AI[1]<n-1){AI[2]="Special"; AI[3]=AI0;}
-        }
+       }
      }
      Snor[i][size(Snor[i])+1]=AI;
@@ -5325 +5279 @@
  {
    Snonor=imap(RP,SnonorP);
-   //"T_Snonor="; Snonor;
-   //"T_G="; G;
    for(i=1;i<=size(Snonor);i++)
    {
      DAC=dimComp(Snonor[i][1]);
      Snonor[i][size(Snonor[i])+1]=DAC;
-     if(tax==1)
-     {
-       AINN=AISnonor(Snonor[i][1],GG);
-       Snonor[i][3][3]=AINN;
-      // AQUI ES ON AFEGIM LA ANTIMATGE DE LES NONOR
-     }
+//      if(tax==1)
+//      {
+//        AINN=AISnonor(Snonor[i][1],GG,DD);
+//        Snonor[i][3][3]=AINN;
+//       // AQUI ES ON AFEGIM LA ANTIMATGE DE LES NONOR
+//      }
    }
    for(i=1;i<=size(Snonor);i++)
@@ -5385 +5337 @@
   int n=size(Rx[1][2]);           // number of parameters
   def nv=nvars(RR);               // number of variables
-  int moverdim=nv;               // number of mover variables
+  int moverdim=n;                // number of mover variables
   ideal vmov;                         // mover variables   (bw)
   for(i=1;i<=(size(DD) div 2);i++)
@@ -5404 +5356 @@
   }
   //string("T_nv=",nv,"  moverdim=",moverdim);
-//  "T_aixo es nou";
 //  for(i=1;i<=nv;i++)
 //  {
@@ -5414 +5365 @@
   ideal bu;                               // ideal of all variables   (u)
   for(i=1;i<=nv;i++){bu[i]=var(i);}
-  ideal mv;                            // ideal of mover variables
-  for(i=1;i<=nv;i++){mv[size(mv)+1]=var(i);}
+  ideal mv;
+// ULL
+// ideal of mover varibles
+//  for(i=1;i<=nv;i++){mv[size(mv)+1]=var(i);}
+   for(i=1;i<=nv;i++){mv[size(mv)+1]=var(i);}
 
    // Searching the basis associated to C
@@ -5431 +5385 @@
    if(te==1){"ERROR";}
    def B=G[j0][2];  // Aixo aniria be per les nonor
-   //"T_B=G[j0][2]="; B;
-   //string("T_k0=",k0," G[",j0,"]="); G[j0];
 
    // Searching the elements in Q[v_m]  on basis different from B that are nul there
@@ -5614 +5566 @@
   int n=size(Rx[1][2]);           // number of parameters
   def nv=nvars(RR);               // number of variables
-  int moverdim=nv;                     // number of mover variables
+  int moverdim=n;                // number of parameters
   ideal vmov;                         // mover variables   (bw)
 
@@ -5635 +5587 @@
   ideal bu;                               // ideal of all variables   (u)
   for(i=1;i<=nv;i++){bu[i]=var(i);}
-  ideal mv;                            // ideal of mover variables
+  ideal mv;                            // ideal of mover varibles
   for(i=1;i<=nv;i++){mv[size(mv)+1]=var(i);}
 
@@ -5652 +5604 @@
    if(te==1){"ERROR";}
    def B=G[j0][2];
-   //"T_B=G[j0][2]="; B;
-   //string("T_k0=",k0," G[",j0,"]="); G[j0];
    return(B);
 }
@@ -5718 +5668 @@
    if(te==1){"ERROR";}
    def B=G[j0][2];     // basis associated to C
-   //"T_B="; B;
 
   // Searching the elements in Q[vmov]  on bases different from B that are nul there
@@ -5776 +5725 @@
   poly kkk=1;
   if(size(NN)==0){NN[1]=kkk;}
-  //"T_NN="; NN;
 
  // Union of F and B
@@ -5783 +5731 @@
    B[size(B)+1]=F[i];
  }
- //"T_B+F="; B;
 
   // Reducing  basis B modulo C  in the ring PR
@@ -5797 +5744 @@
     BBR[i]=reduce(BB[i],CC);
   }
-  //"T_BBR="; BBR;
 
   // Selecting the elements of the ideal in Q[v]
@@ -5810 +5756 @@
     if(subset(variables(BBR[i]),vv)){BR[size(BR)+1]=BBR[i];}
   }
-  //"T_BR="; BR;
   // setring PR;
   // def BR=imap(RP,BRv);
@@ -5836 +5781 @@
    }
   }
-  //"T_BP="; BP;
 
   //  Obtaining Am, the anti-image of C on vmov
@@ -5847 +5791 @@
     if (subset(variables(A[i]),vm)){Am[size(Am)+1]=A[i];}
   }
-  //"T_Am="; Am;
-
 
   list AIM=dimM(Am,nv,nm);
@@ -5871 +5813 @@
   Rx[3][1][2]=iv;
    def DM=ring(Rx);
-  //"Rx="; Rx;
   setring(DM);
   ideal KKMD=imap(RR,KKM);
@@ -5917 +5858 @@
   ideal vpar;
   ideal vvar;
-  //"T_n="; n;
-   //"T_nv="; nv;
   for(i=1;i<=n;i++){vpar[size(vpar)+1]=par(i);}
   for(i=1;i<=nv;i++){vvar[size(vvar)+1]=var(i);}
-  //string("T_vpar = ", vpar," vvar = ",vvar);
   def P=ring(Rx[1]);
   Rx[1]=0;
@@ -5932 +5870 @@
   //string("T_vvpar = ",vvpar);
   ideal B=std(FF);
-  //"T_B="; B;
   ideal Bel;
-  //"T_vvpar="; vvpar;
   for(i=1;i<=size(B);i++)
   {
     if(subset(variables(B[i]),vvpar)) {Bel[size(Bel)+1]=B[i];}
   }
-  //"T_Bel="; Bel;
   list H;
   list FH;
@@ -5976 +5911 @@
 //               The third element tax is:
 //                 for normal point components, tax=(d,taxonomy,anti-image)
-//                    being d=dimension of the anti-image on the mover variables,
+//                    being d=dimension of the anti-image on the mover varaibles,
 //                           taxonomy='Normal'  or  'Special', and
 //                           anti-image=ideal of the anti-image over the mover variables
@@ -6012 +5947 @@
         in Q[x1,..,xn][u1,..,um],
         (x=tracer variables, u=mover variables).
-        The number of tracer variables is n=dim(space).
-        The mover variables can be restricted by the user to the last
-        k variaboes by adding the option \"moverdim\",k
-        (Inverts the concept of parameters and variables of
-        the ring).
+        The tracer variables are x1,..xn = dim(x-space).
+        By default, the mover variables are the last n u-variables.
+        Its number can be forced by the user to the last
+        k variables by adding the option \"moverdim\",k.
+        Nevertheless, this option is recommended only
+        to experiment, and can provide incorrect taxonomies.
 OPTIONS: An option is a pair of arguments: string, integer.
         To modify the default options, pairs of arguments
@@ -6025 +5961 @@
         \"moverdim\", k  to restrict the mover-variables of the
         anti-image to the last k variables.
-        By default k is equal to the number of u-variables,
-        The restriction to a smaller value
-        can produce an error in the character
+        By defaulat k is equal to the last n u-variables,
+        We can experiment with a different value,
+        but this can produce an error in the character
          \"Normal\" or \"Special\" of a locus component.
 
-        \"grobcov\", list of the previous computed grobcov(F).
+        \"grobcov\", L, where L is the list of a previous computed grobcov(F).
         It is to be used when we modify externally the grobcov,
         for example to obtain the real grobcov.
-
-        \"anti-image\",0  if the anti-image is not to be
-        shown for \"Normal\" components.
 
         \"comments\", c: by default it is 0, but it can be set
         to 1.
 RETURN: The output is a list of the components:
-        ((p1,(p11,..p1s_1),tax_1),..,(pk,(pk1,..pks_k),tax_k)
+        ((p1,(p11,..p1s_1),tax_1), .., (pk,(pk1,..pks_k),tax_k)
         Elements 1 and 2 of a component represent the
         P-canonical form of the component.
@@ -6105 +6038 @@
   ideal vmov;
   int nv=nvars(RR);                                  // number of variables
-  int moverdim=nv; //size(ringlist(RR)[1][2]);   // number of parameters
-  if(moverdim>nv){moverdim=nv;}
+ // int moverdim=nv; //size(ringlist(RR)[1][2]);   // number of parameters
+  int moverdim=size(ringlist(RR)[1][2]);   // number of parameters
+    if(moverdim>nv){moverdim=nv;}
   // for(i=1;i<=nv;i++){vmov[size(vmov)+1]=var(i);}
   int version=2;
@@ -6117 +6051 @@
     if(DD[2*i-1]=="moverdim"){moverdim=DD[2*i];}
     if(DD[2*i-1]=="vmov"){vmov=DD[2*i];}
-    if(DD[2*i-1]=="version"){version=DD[2*i];}
+    // if(DD[2*i-1]=="version"){version=DD[2*i];}
     if(DD[2*i-1]=="comment"){comment=DD[2*i];}
     if(DD[2*i-1]=="grobcov"){GG=DD[2*i];}
-    if(DD[2*i-1]=="anti-image"){tax=DD[2*i];}
-  }
+  }
+  // if(version != 2){string("versions 0 and 1 are not available"); version=2;}
   for(i=1;i<=moverdim;i++){vmov[size(vmov)+1]=var(i+nv-moverdim);}
   if(size(GG)==0){GG=grobcov(F);}
-  //"T_GG=grobcov(F)="; GG;
   int j; int k; int te;
   def B0=GG[1][2];
@@ -6130 +6063 @@
   list nGP;
   if (equalideals(B0,ideal(1)) )
-  {
-    if(version==2){return(locus2(GG,F,DD));}
-    else{return(locus0(GG,DD));}
-  }
+  {return(locus2(GG,F,DD));}
+    // if(version==2){return(locus2(GG,F,DD));}
+    //   else{return(locus0(GG,DD));}
+    // }
   else
   {
-    n=nvars(R);
+    n=nvars(RR);
     ideal vB;
     ideal N;
@@ -6195 +6128 @@
   if(version==2)
   {
-    //"T_nGP="; nGP;
     def LL=locus2(nGP,F,DD);
   }
@@ -6402 +6334 @@
        ideal C=g_1(u_1,..u_m),..,g_s(u_1,..u_m);
        envelop(F,C[,options]);   where s<m.
+       x1,..,xn are the trtacer variables.
+       u_1,..,u_m are the auxiliary variables.
+       By default the las n variables are the mover variables.
 RETURN: The output is a list of the components [C_1, .. , C_n]
        of the locus. Each component is given by
@@ -6421 +6356 @@
        To modify the default options,
        pairs of arguments -option name, value- of valid options
-       must be added to the call. The algorithm allows the
-       following option as pair of arguments:
+       must be added to the call.
+
+       The algorithm allows the following options as pair of arguments:
        \"comments\", c: by default it is 0, but it can be set to 1.
        \"anti-image\", a: by default a=1 and the anti-image is
        shown also for \"Normal\" components.
        For a=0, it is not shown.
+       \"moverdim\", k: by default it is equal to n, the number of
+       x-tracer variables.
 NOTE: grobcov and locus are called internally.
        The basering R, must be of the form Q[x][u]
@@ -6472 +6410 @@
   int ng=size(C);
   ideal S=F;
-  //"T_C="; C;
   for(i=1;i<=size(C);i++){S[size(S)+1]=C[i];}
-  //"T_S="; S;
   int s=nv-ng;
   if(s>0)
@@ -6480 +6416 @@
     matrix M[ng+1][ng+1];
     def cc=comb(nv,ng+1);
-    //string("nv=",nv," ng=",ng," s=",s);
-    //"T_cc="; cc;
     poly J;
     for(k=1;k<=size(cc);k++)
@@ -6589 +6523 @@
        See book
        A. Montes. \"The Groebner Cover\":
+OPTIONS: \"moreinfo\",n  n=0 is the default option, and
+       only the segment of the top of the component is shown.
+       n=1  makes the result to shown all the segments.
 NOTE:  grobcov is called internally.
 KEYWORDS: geometrical locus; locus; envelop; associated tangent
@@ -6614 +6551 @@
   {
     if(DD[2*i-1]=="vmov"){vmov=DD[2*i];}
-    if(DD[2*i-1]=="version"){version=DD[2*i];}
+//    if(DD[2*i-1]=="version"){version=DD[2*i];}
     if(DD[2*i-1]=="comment"){comment=DD[2*i];}
     if(DD[2*i-1]=="familyinfo"){familyinfo=DD[2*i];}
@@ -6652 +6589 @@
  //if(comment>0){"System S before grobcov ="; S;}
   def G=grobcov(S,DD);
-  //"T_G=";G;
   list GG;
   for(i=2;i<=size(G);i++)
@@ -6659 +6595 @@
   }
   G=GG;
-  //"T_G=";G;
   if(moreinfo>0){return(G);}
   else
@@ -6711 +6646 @@
 }
 
-proc FamElemsAtEnvCompPoints(poly F,ideal C, ideal E)
+proc FamElemsAtEnvCompPoints(poly F,ideal C, ideal E,list #)
 "USAGE: FamElemsAtEnvCompPoints(poly F,ideal C,ideal E);
        poly F must be the family of hyper-surfaces whose
@@ -6740 +6675 @@
        The segment is the component and is given in Prep.
        Fixing the values of (x_1,..,x_n) inside E, the basis
-       allows to determine the values of the parameters
+       allows to detemine the values of the parameters
        (u_1,..u_m), of the hyper-surfaces passing at a point
        of E. See the book
        A. Montes. \"The Groebner Cover\" (Discussing
        Parametric Polynomial Systems).
+OPTIONS: \"moreinfo\",n  n=0 is the default option, and
+       only the segment of the top of the component is shown.
+       n=1  makes the result to shown all the segments.
 NOTE: grobcov is called internally.
        The basering R, must be of the form Q[a][x]
@@ -6753 +6691 @@
   int i;
   int moreinfo=0;
+  list DD=#;
+  for(i=1;i<=(size(DD) div 2);i++)
+  {
+    if(DD[2*i-1]=="vmov"){vmov=DD[2*i];}
+//    if(DD[2*i-1]=="version"){version=DD[2*i];}
+    if(DD[2*i-1]=="comment"){comment=DD[2*i];}
+    if(DD[2*i-1]=="familyinfo"){familyinfo=DD[2*i];}
+    if(DD[2*i-1]=="moreinfo"){moreinfo=DD[2*i];}
+  };
   ideal S=C;
   ideal EE=E;
@@ -7181 +7128 @@
     }
      // B=reduced basis on CR
-     //"T_PR="; PR;
-     //"T_CR="; CR;
-     //"T_B="; B;
     if(rep==1){return(list(lcc,B,CR));}
     else{return(list(lcc,B,PR));}
@@ -7284 +7228 @@
     {
       G[size(G)+1]=G0;
-      //"T_G0="; G0;
       N=G0[3][1][2];
-      //"T_N="; N;
       for(i=1;i<=size(N);i++)
       {
@@ -7294 +7236 @@
           Epend[size(Epend)+1]=N[i];
         }
-        //"T_i="; i;
-      }
-      //"T_Etot="; Etot;
-      //"T_Epend=";Epend;
+      }
     }
   }
@@ -7373 +7312 @@
   int i; int j;
   ideal J=idminusid(E,N);
-  //"T_J="; J;
   for(i=1;i<=size(F);i++)
   {
@@ -7525 +7463 @@
   setring(RP);
   def SP=imap(RR,S);
-  //"T_SP="; SP;
-  //"T_typeof(SP[1])="; typeof(SP[1]);
   ideal EP;
   EP=SP[1];
@@ -7678 +7614 @@
     int r=m div 2;
     if(m mod 2==0){r=r-1;}
-    //"L0="; L0;
-     for(i=1;i<=r;i++)
+    for(i=1;i<=r;i++)
     {
       G1=grobcov(F,"null",L0[2*i],"nonnull",L0[2*i+1],"rep",1);
@@ -7775 +7710 @@
 ADGT(H,T,H1,T1);
 
-// Now using diference of constructible sets for negative hypothesis and thesis
+// Now using difference of constructible sets for negative hypothesis and thesis
 
 ADGT(H,T,H1,T1,"neg",1);
@@ -7790 +7725 @@
 // Vertices of the triangle: A(-2,0), B(2,0), C(2a,2b)
 
-// Height foot: A1(x1,y1),
-// Height foot: B1(x2,y2),
-// Height foot: C1(2a,0)
+// Heigth foot: A1(x1,y1),
+// Heigth foot: B1(x2,y2),
+// Heigth foot: C1(2a,0)
 
 // Middle point BC:  A2(a+1,b)
@@ -7862 +7797 @@
     list G2=grobcov(F,"rep",1);
     def L2=Grob1Levels(G2);
-    //"L2="; L2;
     ideal FN=T1;
     if(not(equalideals(H1,ideal(1))))
@@ -7877 +7811 @@
       list G3=grobcov(F,"rep",1);
       def L3=Grob1Levels(G3);
-      //"L3="; L3;
     }
     def LL=DifConsLCSets(L2,L3);
-    //"LL="; LL;
     LL=ConsLevels(LL);
     LL=Levels(LL);
-     //"LL="; LL;
     if(rep==1){return(LL);}
     else